According to Legends (C-canon) game Star Wars: The Force Unleashed, the Rebellion's start was as follows:

Galen Marek, pretending to be a Jedi, convinced Senators Bail Organa, Mon Mothma, and Garm Bel Iblis, and General Kota, to start a formal open Rebellion Alliance (Corellian Treaty in ~2 BBY).

In reality, Marek was Darth Vader's secret apprentice, and the whole thing was part of a plan to lure all the potential rebels into the open, under the pretense of creating an alliance to destroy the Emperor (and in reality, to flush them out and crush them).

The plan initially succeeded - at the signing, Vader and stormtroopers arrested Bail Organa, Mon Mothma, and Garm Bel Iblis, and took them to Death Star I to meet the Emperor and their doom.

This was disrupted when Galen Marek switched to the Light side, and at the cost of his own life bought the escape of the leaders of the soon-to-start Rebellion.

Question is: that was 2 years before events of SW:ANH, and for those 2 years Vader and Emperor knew that Bail Organa was a rebellious traitor.

Why didn't Palpatine crush (either arrest, or assassinate) Bail Organa (or the others, for that matter - but with Organa, he knew where to find him, on Alderaan or in the Senate) in between 2BBY and Alderaan's destruction during ANH?

Even for the Emperor, it would be difficult to move against the leader of a planet with as uch influence as Alderaan, and an arrest and trial posed the nasty possibility that Organa would use his rhetorical skill to humiliate his prosecutors and appear the victim (Hermann Goering at Nuremberg, who, despite being guiltier than sin, somehow came out of the trial looking like a hero to the average German). Assassination was an option, and Mara Jade indicated that Palpatine considered using her for such, but "found something better," in Spectre of the Past. Presumably that was the Death Star.
– James SheridanDec 27 '14 at 1:04

Presumably because he was an important and influential Senator, one who had supported Palpatine on a number of occasions. Note that it's only after the Senate is disbanded that Tarkin turns Alderaan into fine powder.
– ValorumDec 27 '14 at 1:06

1

I don't think that they knew that he was a leader of the rebellion it doesn't fit with A New Hope at the beginning Vader was trying to prove that Leia was a member of the Rebel Aliance but had no proof until he captured the Tantavive IIII
– The MandolorianMar 15 '16 at 7:56

2 Answers
2

Because Vader and the Emperor have not yet eliminated the need for them.

As you said, this takes place Two Years prior to the events of Episode IV. Despite the Emperor's immense power over the Galaxy, he is still reliant the Senatorial council to keep regions of space from objecting to his power - as long as they are around, order can be maintained.

The point of this exercise, of the deception, was to draw out potential rebels and execute them before a rebellion could be carried out - but with this plot foiled, and without a weapon to strike terror into the hearts of the Galaxy's rulers, they have no option but to pretend it never happened.

In any case, knowing that the Death Star WOULD be operational in 2 years, and that the Senate would be terminated at that time (it was his decision after all) the effort to eliminate them individually would be wasted, when they could simply intimidate the fight out of them, destroy anyone who opposed them, and hunt down and wipe out any open rebellion that emerges with their new super weapon.

And he would've gotten away with it too, if not for that meddling farmboy and his droid.

Between 2 BBY and Alderaan's destruction, we don't have canon information whether Bail Organa used to dance with Darth Vader or not. In a canon version in which Bail Organa's secret was revealed, Bail Organa would obviously don't go in public where he could easily be crushed by the Empire.

Note: Empire did know the identity of lots of rebel leaders, but knowing is one thing and hunting them down is another. In the movies, the battle between Empire and Rebel Alliances can show the position of such leaders. They were certainly not ordinary ants to easily be crushed. Crushing leaders needed the same efforts as crushing Rebel Alliance.

When Empire destroyed Alderaan, it's possible that known presence of Bail Organa on Alderaan added some points to the Empire's motivation for destroying Alderaan.